On the origins of transport inefficiencies in mesoscopic networks.

A counter-intuitive behavior analogous to the Braess paradox is encountered in a two-terminal mesoscopic network patterned in a two-dimensional electron system (2DES). Decreasing locally the electron density of one channel of the network paradoxically leads to an increased network electrical conductance. Our low temperature scanning gate microscopy experiments reveal different occurrences of such puzzling conductance variations, thanks to tip-induced localized modifications of electron flow throughout the network's channels in the ballistic and coherent regime of transport. The robustness of the puzzling behavior is inspected by varying the global 2DES density, magnetic field and the tip-surface distance. Depending on the overall 2DES density, we show that either Coulomb Blockade resonances due to disorder-induced localized states or Fabry-Perot interferences tuned by the tip-induced electrostatic perturbation are at the origin of transport inefficiencies in the network, which are lifted when gradually closing one channel of the network with the tip.

Recurrent Quantum Scars in a Mesoscopic Graphene Ring.

When coherent charge carriers cross micron-scale cavities, their dynamics can be governed by a few resonant states, also called "quantum scars", determined by the cavity geometry. Quantum scars can be described using theoretical tools but have also been directly imaged in the case of high-quality semiconductor cavities as well as in disordered graphene devices, thanks to scanning gate microscopy (SGM). Here, we discuss spatially resolved SGM images of low-temperature charge transport through a mesoscopic ring fabricated from high-quality monolayer graphene lying on top of hexagonal boron nitride. SGM images are decorated with a pattern of radial scars in the ring area, which is found to evolve smoothly and reappear when varying the charge-carrier energy. The energies separating recurrent patterns are found to be directly related to geometric dimensions of the ring. Moreover, a recurrence is also observed in simulations of the local density of states of a model graphene quantum ring. The observed recurrences are discussed in the light of recent predictions of relativistic quantum scars in mesoscopic graphene cavities.